Skip to main content
SpringerLink
Log in

An exact solution of Laplace's equation for cuspidal geometry

Application to liquid metal ion sources

  • Contributed Papers
  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

An exact solution of Laplace's equation is obtained for a system of conducting electrodes with cuspidal symmetry. The significance of this result in predicting and verifying the equilibrium configuration of a rotationally symmetric conducting fluid subject to electrostatic stress is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.R. Pierce:Theory and Design of Electron Beams (van Nostrand, Princeton, NJ 1954)

    Google Scholar 

  2. O. Klemperer:Electron Optics, 3rd. ed. (Cambridge University Press, Cambridge 1971)

    Google Scholar 

  3. D. Alpert, D.A. Lee, E.M. Lyman, H.E. Tomaschke: J. Vac. Sci. Technol.1, 34 (1964)

    Google Scholar 

  4. C.B. Duke: Tunneling in Solids,Solid State Physics, Suppl. 10 (Academic Press, New York 1969)

    Google Scholar 

  5. T.E. Feuchtwang, P.H. Cutler, N.M. Miskovsky, A.A. Lucas: “Electron Tunneling Theory and Non-Linear Transport in Junctions and Microstructures.” InQuantum Metrology and Fundamental Physical Constants (Plenum Press, New York 1983)

    Google Scholar 

  6. H. Gaubi, P. Sudraud: “New Results About in situ TEM Observation of the Emission Region in Liquid Metal Ion Source,” published in Proceedings of the 29th Intern. Field Emission Symposium, Göteborg, Sweden, ed. by H.O. Andrén and H. Nordén (Almqvist and Wiksell, Stockholm 1982); see also G. Benassayay, P. Sudraud, “A W/Liquid Metal Interface Treatment Extends LMIS to Non-Wetting Materials,” presented at the 30th Intern. Field Emission Symposium, Univ. of Pennsylvania, Philadelphia, PA (1983). Photographs were presented in this talk that clearly showed a well-defined cuspidal structure of the emitter surface

    Google Scholar 

  7. G. Taylor: Proc. R. Soc. (London)280 A, 383 (1964)

    Google Scholar 

  8. N. Sujatha, P.H. Cutler, E. Kazes, J.P. Rogers, N.M. Miskovsky: Appl. Phys. A32, 55 (1983)

    Google Scholar 

  9. N. Sujatha, P.H. Cutler, E. Kazes, N.M. Miskovsky: “New Analysis for the Equilibrium Configuration of a Conducting Fluid in an Electrostatic Field,” presented at the 30th Intern. Field Emission Symposium, Univ. of Pennsylvania, Philadelphia, PA (1983)

    Google Scholar 

  10. P.M. Morse, H. Feshbach:Methods of Theoretical Physics (McGraw-Hill, New York 1953)

    Google Scholar 

  11. E.W. Hobson:Theory of Spherical and Ellipsoidal Harmonics (Cambridge University Press, Cambridge 1931)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, The Pennsylvania State University, 16802, University Park, PA, USA

    N. M. Miskovsky, P. H. Cutler & T. E. Feuchtwang

  2. Altoona Campus, 16603, Altoona, PA, USA

    N. M. Miskovsky

Authors
  1. N. M. Miskovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. H. Cutler
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. E. Feuchtwang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported in part by the Division of Materials Research, National Science Foundation, Grant No. DMR-8108829

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miskovsky, N.M., Cutler, P.H. & Feuchtwang, T.E. An exact solution of Laplace's equation for cuspidal geometry. Appl. Phys. A 33, 205–207 (1984). https://doi.org/10.1007/BF00618757

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00618757

PACS

Search

Navigation